Multiple Positive Solutions to Nonlinear Schrödinger Equations with Competing Potential Functions

In this paper we obtain multiple positive solutions of the nonlinear elliptic equation −h2Δu+V(x)u=K(x)|u|p−2u+Q(x)|u|q−2u, x∈RN, where V, K, Q are competing potential functions. We relate the number of solutions with the topology of the global minima set of a suitable ground energy function and imp...

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Bibliographic Details
Published in:Journal of Differential Equations 2000-01, Vol.160 (1), p.118-138
Main Authors: Cingolani, Silvia, Lazzo, Monica
Format: Article
Language:English
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Summary:In this paper we obtain multiple positive solutions of the nonlinear elliptic equation −h2Δu+V(x)u=K(x)|u|p−2u+Q(x)|u|q−2u, x∈RN, where V, K, Q are competing potential functions. We relate the number of solutions with the topology of the global minima set of a suitable ground energy function and improve a recent existence result of X. Wang and B. Zeng (1997, SIAM J. Math. Anal.28, 633–655).
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.1999.3662